Trailing 11-9 late in the fourth quarter, Ivovic notched his third goal of the game for Montenegro before Janovic slotted the equalizer in the upper left corner with 51 seconds to go. Goalkeeper Milos Scepanovic then denied Serbia's Andrija Prlainovic from close-range in the closing seconds to preserve the draw.
"It was (a) very difficult, physical game," Montenegro captain Nikola Janovic said. "I think we didn't begin the match well, made a lot of mistakes, but after that we play our game and at the end I think we had a chance for a win. But this result is OK."
The draw leaves Serbia in second place in Group B, one point behind the United States, which beat Britain 13-7 with four goal from Tony Azevedo to remain unbeaten in London. Montenegro is third with three points, but has its two weakest opponents to come — Romania and Britain.
Montenegro was playing catch-up the whole game after falling behind in the first quarter on a Prlainovic goal — his first of his five on the afternoon for Serbia.
But in a game that included as many shots to the face and elbows to the throat as it did goals, the Montenegro players managed to get back into the contest with sharp shooting from Ivovic and Janovic.
The ferocity of the match stemmed from the countries shared history. Five players in the pool Thursday — three from Montenegro and two from Serbia — won silver as teammates for Serbia and Montenegro at the 2004 Olympics, two years before the countries separated.
"Every game against Montenegro is very stressful and very emotional," said Serbia's Filip Filipovic. "We were until yesterday, if I can say, in the same room and now we have to compete for who is going to be better and there is a very big rivalry between us."
Hungary recorded its first victory at the London Games, pulling away in the second half to beat Romania 17-15. Thursday's victory was a big one for the three-time defending Olympic champions, coming after losses in their first two matches to Serbia and Montenegro.
Norbert Hosnyanszky and captain Peter Biros chipped in with three goals each for Hungary, which earned two points in Group B with the win to keep alive its chances of advancing to the quarterfinals.
"Finally," Hungary star Tamas Kasas said of the win, adding that the team has to improve its "horrible" play on the defensive end.
"I don't know why but in defence things are not working well. We have to try something else," he said.
In Group A, Spain earned an easy 13-9 win over Australia behind goals from 10 different players. Every outfield player except Balazs Sziranyi Somogyi scored for the Spanish, who is looking for their first Olympic medal in men's water polo since winning gold in 1996.
"We are really happy because we think that more than the result, the feeling is that the team is playing together," said Filipe Perrone Rocha, who scored two goals to raise his tournament tally to nine.
Spain's win comes after a disputed 8-7 loss on Tuesday to Croatia, in which the officials didn't recognize a last-gasp Spanish shot that appeared to cross the line to level the game at the buzzer. Spain lodged an appeal to FINA, which the sport's governing body rejected.
With four points from three matches, Spain is two points behind Group A leader Croatia, which pulled away in the second half for an 11-6 win Thursday over 2011 world champion Italy.
Sandro Sukno and Miho Boskovic scored three goals each for Croatia, which is one of the leading medal contenders in a deep men's field.
Greece also improved its chances of reaching the knockout stage with its easy 11-4 win over Kazakhstan behind five goals from Ioannis Fountoulis, giving the Greeks three points from three Group A games, with Spain and Australia still to come in the preliminary stage.
Kazakhstan is winless and at the bottom of the group.
Ryan Lucas can be reached on twitter at www.twitter.com/relucasz